In this seminar, Prof. John Etnyre
will begin this talk by discussing a classical question concerning
periodic motions of particles in classical physics. In trying to better
understand this question we will develop the notion of a symplectic
structure. This is a fundamental geometric
object that provides the "right way" to think about classical mechanics,
and many many other things too. We will then indicate how modern ideas
can be used to give, at least partial, answers to our initial naive
questions about periodic motions.